Minimal Feedback Vertex Sets in Honeycomb Networks

Abstract

A vertex subset of a graph G is called a feedback vertex set if its removal results in an acyclic subgraph. The feedback vertex numberï´ (G) is the cardinality of the minimum feedback vertex set of G , which is an important parameter of interconnection network topology. In this paper, we determine the feedback numbers of Honeycomb mesh n HM and Honeycomb torus n HT , i.e. 2 ( ) 9 / 2 15n/2 4 n ï´ HM  n   and 2 ( ) 9 / 2 9 / 2 2 n ï´ HT  n  n  . Comparing these results with those of Zhou, we find thatï´ (H) is related to the boundary of Honeycomb network H .